So I am theoretically planning to make an RC differentiator circuit but I'm still a rookie with it so if someone can help me it would be appreciated.
The condition is defined by time domain exponential behavior and frequency domain.
You requirements must include some specification to be below some cutoff frequency or exponential constant T=RC with some tolerance such T defines the voltage decay to 64% of target.
e.g. differentiator for f < fo/10 or 20 dB down or T=1/fo=1/2piRC
The current phase leads voltage by 90 degrees.
e.g. a High Pass Filter performs differentiation (to some tolerance) below fo/10 typ.
A ideal differentiator has no upper limit in frequency gain +6dB/octave.
Other equivalent conditions to + 6dB/octave are +20dB/octave for the frequency range of interest.
It can block DC current with a series C with a shunt R
b) or shunt DC current to 0 volts with a series R and a shunt L.